Definition 3.10 (Rate-distortion function [1]}) 

Let \(\mathcal {X}\)  and \(\mathcal {Y}\)  be a pair of discrete spaces and \(*{C}(\mathcal {X},\mathcal {Y})\)  be the space of all channels encoding from \(\mathcal {X}\)  to \(\mathcal {Y}\) . Suppose \(X\)  is a random variable defined over \(\mathcal {X}\)  and fix a \(d^*\in \mathbb {R}^+\) .
